Six rounds of the NFL Draft had passed and Devante Downs had grown tired of waiting.

A few months earlier, he was one of the leading tacklers in the Pac-12, a standout linebacker at California who was told he’d become a second- or third-round pick if he kept up his play. But six rounds had gone by and Downs still hadn’t heard his name called, a byproduct of a knee injury he suffered before his college season was halfway over.

So as the draft continued with a seventh and final round, Downs left the house with his father to go to the grocery store.

“My dad wanted something to eat because there is no food at my house,” Downs explained.

Two-hundred, twenty-five picks into the draft, the Vikings finally ended Downs’ wait while he was in the grocery store by making him their final selection in an eight-person draft class.

“I heard I could have gone on Day 2 with where I was before I was injured,” Downs said. “But things change. I...